Talk:Kite's color notation/Temperament names: Difference between revisions
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:: Okay, I see the edit. I think you've misunderstood my concern, though. It probably comes as a surprise because it runs counter to prevailing thinking about this topic. But Dave Keenan and I did a ton of research and discussion on this recently and we've come to the conclusion that temperaments ''cannot have torsion''. It is not a problem to avoid, but an impossibility. Certainly, you can take a comma like {{vector|-4 4 -1}} and multiply it by 2 to get {{vector|-8 8 -2}}. Our point is that while that has an effect on periodicity blocks, it has no effect on temperaments, because tempering out {{vector|-8 8 -2}} implies tempering out {{vector|-4 4 -1}}. On the other hand, temperaments ''can'' have ''con''torsion, because {{vector|24 38 56}} does mean something musically different in RTT than {{vector|12 19 38}}; however, because temperaments can't have torsion, we don't think it makes sense to call this effect "contorsion"; we call it "enfactoring" instead. Actually, the section of my new page I linked you to in the previous post may not have been the best introduction to our finding. Please try this one instead: [[Canonical_form#enfactored.2C_to_replace_contorted]] --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 01:20, 30 September 2021 (UTC) | :: Okay, I see the edit. I think you've misunderstood my concern, though. It probably comes as a surprise because it runs counter to prevailing thinking about this topic. But Dave Keenan and I did a ton of research and discussion on this recently and we've come to the conclusion that temperaments ''cannot have torsion''. It is not a problem to avoid, but an impossibility. Certainly, you can take a comma like {{vector|-4 4 -1}} and multiply it by 2 to get {{vector|-8 8 -2}}. Our point is that while that has an effect on periodicity blocks, it has no effect on temperaments, because tempering out {{vector|-8 8 -2}} implies tempering out {{vector|-4 4 -1}}. On the other hand, temperaments ''can'' have ''con''torsion, because {{vector|24 38 56}} does mean something musically different in RTT than {{vector|12 19 38}}; however, because temperaments can't have torsion, we don't think it makes sense to call this effect "contorsion"; we call it "enfactoring" instead. Actually, the section of my new page I linked you to in the previous post may not have been the best introduction to our finding. Please try this one instead: [[Canonical_form#enfactored.2C_to_replace_contorted]] --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 01:20, 30 September 2021 (UTC) | ||
::: I totally agree about torsion. Been thinking that way for years. You can't hear periodicity blocks! Someone explained to me once that it's mathematically possible to temper the two {{vector|-4 4 -1}}'s differently, but that's silly. That would be an irregular temperament, but the "R" in RTT means regular. | |||
::: I agree about contorsion too. Contorsion is like saying that all 12edo music is really in 24edo, but half the notes don't happen to get used. :) | |||
::: As for this article, sure, torsion in the comma list (in the sense that the pivot product is bigger than it needs to be) is not at all a problem musically or mathematically. Rule #2 says to avoid torsion only as a means to getting a canonical name for the temperament. | |||
::: I will read your articles when I get a chance. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 01:46, 30 September 2021 (UTC) | |||